Despite significant experimental and theoretical efforts, a fundamental understanding of how the chemical structure influences various dynamic processes in glass-forming materials and polymers remains a topic of active discussion. The present study analyzes the influence of polar interactions on the temperature dependences of segmental and chain dynamics in polymers. We found that segmental dynamics slow down (the glass transition temperature T-g increases) and have steeper temperature dependence (higher fragility index m) when a polar group is attached directly to the polymer backbone. However, when a polar group is separated from the backbone by a side group, both T-g and m become complex functions of the monomer's polarity and the relative position of the polar group. Our analysis revealed unexpected effect of polar interactions on chain dynamics: chain modes in polar polymers are coupled to the segmental dynamics stronger than in nonpolar polymers with similar fragilities. This results in a steeper temperature dependence of chain dynamics in polar polymers. How the polar interactions affect the coupling of chain and segmental modes remains unclear.